Answer:
Explanation:
given,
Temperature of heat engine operate between
Th (temperature in hot reservoir) and Tc(temperature in cold reservoir)
amount of heat released to = Qc
to find maximum amount of work = ?
now,
efficiency of heat engine
now,
maximum work =
above expression gives the expression of maximum amount of work.
(a)
At a distance r=R from the centre of the planet, there is no effect due to the outer shell: so, the gravitational field strength at r=R is only determined by the gravity produced by the core of the planet.
So, the strength of the gravitational field is given by
where
G is the gravitational constant
M = 6.24 × 10^24 kg is the mass of the core of the planet
R = 4.11 × 10^6 m is the radius of the core
Substituting into the equation, we find
(b)
at distance r=3R from the centre, the particle feels the effect of gravity due to both the core of the planet and the outer shell between R and 2R.
So, we have to consider the total mass that exerts the gravitational attraction at r=3R, which is the sum of the mass of the core (M) and the mass of the shell (4M):
M' = M + 4M = 5M
Therefore, the gravitational acceleration at r=3R will be
And susbstituting
g = 24.6 m/s^2
found in the previous part, we find
Recall that
where and
are the initial and final velocities, respecitvely;
is the acceleration; and
is the change in position.
So we have
(Normally, this equation has two solutions, but we omit the negative one because the car is moving in one direction.)